Totally-Endoscopic Coronary Artery Bypass operations, which should ideally be entirely performed with a robotic surgical assistant, currently suffer from a high rate of conversion to more traditional procedures, partly due to the difficulty of identifying the coronary artery that is to be operated upon. One solution to this problem is to guide the surgeon by superimposing models of patients' hearts onto the images provided by the robot. Motivated by the possibility of using motion information to (partially) constrain the registration of the model to the images, this thesis focuses on methods of estimating the motion of salient patches on the myocardial surface.

We begin by introducing an importance sampling algorithm for hypothesising affine patch transformations in a particle filtering framework. The algorithm minimises uncertainty by multiplicatively combining information from multiple patch subregions. We devise a method for handling missing information based on empirical evidence that suggests that certain importance sampling probability ratios grow empirically with the number of subregions.

We then describe methods for calculating the dissimilarity between image regions whilst taking into account specular reflections and illumination changes. We achieve insensitivity to these effects by explicitly removing illumination changes, tentatively masking out specular reflections, and ignoring pixel differences that exceed a percentile of a weighted pixel difference distribution.

Next, we investigate myocardial deformation sequence models, and propose nesting a PCA model of the static deformations within a periodic B-spline-based PCA model of the deformation sequences. We use this model to simulate data sets that we can use to approximate maximum likelihood estimates of some parameters of the particle filter components, and we describe a way of testing whether or not particles have entered low-probability states in which they cease to contribute useful information.

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